Question: Simplify the following expression: $\dfrac{15y^3}{3y^5}$ You can assume $y \neq 0$.
Solution: $ \dfrac{15y^3}{3y^5} = \dfrac{15}{3} \cdot \dfrac{y^3}{y^5} $ To simplify $\frac{15}{3}$ , find the greatest common factor (GCD) of $15$ and $3$ $15 = 3 \cdot 5$ $3 = 3$ $ \mbox{GCD}(15, 3) = 3 $ $ \dfrac{15}{3} \cdot \dfrac{y^3}{y^5} = \dfrac{3 \cdot 5}{3 \cdot 1} \cdot \dfrac{y^3}{y^5} $ $\phantom{ \dfrac{15}{3} \cdot \dfrac{3}{5}} = 5 \cdot \dfrac{y^3}{y^5} $ $ \dfrac{y^3}{y^5} = \dfrac{y \cdot y \cdot y}{y \cdot y \cdot y \cdot y \cdot y} = \dfrac{1}{y^2} $ $ 5 \cdot \dfrac{1}{y^2} = \dfrac{5}{y^2} $